The study of quantum interference effects in low-dimensional semiconductor systems provides critical insights into the phase coherence of charge carriers and the tunability of electronic properties. In graphene nanoribbons and transition metal dichalcogenide (TMDC) constrictions, two prominent interference phenomena—Aharonov-Bohm (AB) and Fabry-Pérot (FP)—dominate the quantum transport regime. These effects are highly sensitive to phase coherence lengths and external electrostatic gating, making them valuable for probing fundamental physics and developing advanced electronic devices.
Aharonov-Bohm interference arises when electrons traverse a closed-loop trajectory, acquiring a phase difference due to an applied magnetic field. In graphene nanoribbons, the AB effect manifests as periodic conductance oscillations with magnetic flux, demonstrating the preservation of phase coherence over micron-scale distances. Experiments on clean, narrow graphene ribbons reveal oscillations with a periodicity corresponding to the magnetic flux quantum h/e, confirming ballistic transport and phase coherence lengths exceeding 1 µm at low temperatures. The gate voltage modulates the Fermi level, altering the electron density and thereby tuning the oscillation amplitude and phase. In TMDC constrictions, such as those in MoS2 or WSe2, the AB effect is observable despite stronger spin-orbit coupling and valley-dependent scattering. The phase coherence length in these materials typically ranges between 100 nm and 500 nm, depending on defect density and temperature.
Fabry-Pérot interference occurs when electrons reflect between two barriers, forming standing waves that modulate conductance as a function of energy. In graphene nanoribbons with well-defined edges, FP resonances appear as periodic conductance oscillations when sweeping the gate voltage. The resonance spacing depends on the length of the cavity between barriers and the Fermi wavelength. For a 100 nm-long cavity, the spacing between adjacent FP peaks can be on the order of 10 meV, reflecting the quantized energy levels of the confined electrons. TMDC constrictions exhibit similar FP interference, though the presence of a bandgap introduces additional complexity. The resonance conditions are influenced by the effective mass and the gate-tunable carrier density, leading to distinct patterns compared to graphene.
The phase coherence length is a key parameter governing the visibility of interference effects. In high-quality graphene nanoribbons, phase coherence lengths of 1-3 µm have been reported at temperatures below 4 K, decreasing with rising temperature due to enhanced electron-phonon scattering. For TMDCs, phase coherence lengths are generally shorter, often below 500 nm, as a result of stronger intrinsic scattering mechanisms. However, encapsulation in hexagonal boron nitride (hBN) can significantly improve these values by reducing Coulomb scattering from substrate impurities.
Gate tunability plays a crucial role in manipulating interference patterns. In graphene, the Dirac point allows for continuous adjustment of the Fermi level across the charge neutrality point, leading to symmetric electron and hole transport regimes. This tunability enables precise control over FP resonances and AB oscillation phases. In TMDCs, the gate voltage not only modulates carrier density but also affects the valley polarization and spin texture, adding another layer of complexity to interference phenomena. For instance, in monolayer MoS2, the interplay between gate-induced doping and valley-contrasting physics can lead to spin-selective interference patterns.
The following table summarizes key differences between AB and FP interference in graphene and TMDCs:
| Feature | Graphene Nanoribbons | TMDC Constrictions |
|-----------------------|------------------------------------|-----------------------------------|
| Phase Coherence Length | 1-3 µm (low T) | 100-500 nm (low T) |
| AB Oscillation Period | h/e | h/e (with valley/spin modulation)|
| FP Resonance Spacing | ~10 meV (100 nm cavity) | Bandgap-dependent |
| Gate Tunability | Continuous across Dirac point | Affects valley/spin polarization |
Temperature and disorder are critical factors influencing interference visibility. At higher temperatures, inelastic scattering processes degrade phase coherence, smearing out interference patterns. In graphene, temperatures above 30 K often suppress AB oscillations, while FP resonances may persist up to 100 K in high-mobility samples. For TMDCs, the temperature threshold is typically lower due to stronger electron-phonon coupling. Disorder, such as edge roughness or bulk defects, also reduces interference contrast by introducing random phase shifts. Optimized fabrication techniques, such as etching-free transfer methods for graphene or encapsulation in hBN for TMDCs, are essential for achieving clean interference signatures.
The study of these quantum interference effects has implications beyond fundamental research. Gate-tunable AB and FP phenomena can be harnessed for phase-coherent devices, including interferometers, valley filters, and quantum switches. The ability to control interference patterns via electrostatic gating offers a pathway toward reconfigurable nanoelectronic circuits. Furthermore, understanding phase coherence in these materials informs the design of topological and spin-based devices, where maintaining quantum coherence is paramount.
In summary, Aharonov-Bohm and Fabry-Pérot interferences in graphene nanoribbons and TMDC constrictions serve as powerful tools for investigating phase-coherent transport. The differences in phase coherence lengths, gate tunability, and temperature dependence highlight the unique properties of each material system. Advances in material quality and device engineering continue to push the boundaries of observable quantum effects, paving the way for novel applications in quantum electronics.